Q. The area bounded by the curve $x = 4 - y^{2}$ and the $y$-axis is
A) 16 $sq\ units$
B) 32 $sq\ units$
C) $\frac{32}{3}sq\ units\$
D) $\frac{16}{3}\ sq\ units\$
Explanation
(c)
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The required area
$= 2 \times \int_{0}^{4}\sqrt{4 - x}\ dx$
$= {2\left\lbrack \frac{(4 - x)^{3/2}}{3/2} \right\rbrack}_{0}^{4} = 2\left\lbrack - \frac{2}{3} \times 0 + \frac{2}{3}{(4)}^{3/2} \right\rbrack$
$= \frac{32}{2}\ sq\ units$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.